Structure of Complexes Formed by PDADMAC and Sodium Palmitate

CDATA[SELF-ASSEMBLY SYNTHESES AND MESOMORPHIC STRUCTURES INVESTIGATION OF POLYVIOLOGEN-ALIPHATATE SURFACTANT ...
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Structure of Complexes Formed by PDADMAC and Sodium Palmitate Juha Merta,† Vasil M. Garamus,*,‡ Regine Willumeit,‡ and Per Stenius† Helsinki University of Technology, Laboratory of Forest Products Chemistry, Espoo, Finland, and GKSS Research Centre, Geesthacht, Germany Received December 28, 2001. In Final Form: June 6, 2002 The size and structure of complexes formed in dilute aqueous solutions by poly(diallyldimethylammonium chloride), PDADMAC, and sodium palmitate have been investigated by small-angle neutron scattering. Internal contrast variation by using protonated and deuterated surfactants has been performed. Rodlike complex aggregates of polymer and surfactant with lengths of a few thousand angstroms have been observed. The cross section of aggregates (diameter, 50-55 Å) shows a shell structure with an inner surfactant core and an outer polymer shell. There is also a mixing layer of polymer and surfactant. The aggregates are flexible (persistence length of the order of 150 Å). The observed structure of the aggregates does not follow the well-known pearl-necklace model developed for poly(ethylene oxide)/sodium dodecyl sulfate complexes.

Introduction Polymer/surfactant interactions in aqueous solutions have been extensively studied as documented in several recent reviews, for example, refs 1-4. The general picture emerging from these studies is that in dilute solutions surfactant molecules interact cooperatively with the polymers, forming micellar or micellar-like clusters associated with the polymer chain. Association is driven by hydrophobic interactions between the surfactant chains and/or between the chains and hydrophobic moieties on the polymer. Association between ionic surfactants and oppositely charged polyelectrolytes is also entropically driven by the concomitant release of small counterions. Association of poly(diallyldimethylammonium chloride), PDADMAC, with anionic surfactants and mixtures of anionic and nonionic surfactants has been extensively investigated by Dubin and co-workers,5,6 using turbidimetry, dynamic and static light scattering, viscometry, electrophoretic light scattering, microcalorimetry, and other methods. Parameters investigated include ionic strength, micellar charge (fraction of ionic surfactant), polymer molecular weight, and concentrations of polymer and surfactant. The influence of these parameters on association can be summarized as follows: (a) polymers associate with micellar aggregates when the fraction of ionic surfactant in the mixture exceeds a critical value; * Corresponding author. GKSS Research Centre, Abt. WFS-Geb. 03, Max-Planck-Str., 21502 Geesthacht, Germany. Phone: +49 4152 871290. Fax: +49 4152 871356. E-mail: vasyl.haramus@ gkss.de. † Helsinki University of Technology. ‡ GKSS Research Centre. (1) Interactions of Surfactants with Polymers and Proteins; Goddard, E. D., Ananthapadmanadhan, K. P., Eds.; CRC Press: Boca Raton, FL, 1993. (2) Hayakawa, K.; Kwak, J. C. T. In Cationic Surfactants, 2nd ed.; Rubingh, N. D., Holland, P. M., Eds.; Marcel Dekker: New York, 1991; p 189. (3) Saito, S. In Nonionic Surfactants; Schick, M. J., Ed.; Marcel Dekker: New York, 1991; p 881. (4) Robb, I. D. In Anionic Surfactants - Physical Chemistry of Surfactant Action; Lucassen-Reynders, E., Ed.; Marcel Dekker: New York, 1981; p 109. (5) Li, Y.; Dubin, P. L. In Structure and Flow in Surfactant Solutions; Herb, C. A., Prud’homme, R. K., Eds.; ACS Symposium Series 578; American Chemical Society: Washington, DC, 1994; Chapter 23. (6) Xia, J.; Zhang, H.; Rigsbee, D. R.; Dubin, P. L.; Shaikh, T. Macromolecules 1993, 26, 2759.

(b) this critical value depends linearly on the square root of ionic strength; (c) the larger the concentration and/or molecular weight of the polymer, the larger the complexes. The critical fraction of ionic surfactant increases when the length of the ethylene oxide chain of the nonionic surfactant in the surfactant mixture increases.7 Binding of the micelles to the polymer is endenthalpic,8 suggesting that the driving force for micelle formation is entropic. The structure of phase-separated, electrostatically neutral, cross-linked PDADMAC/anionic surfactant complexes (sodium alkyl sulfates) was studied by Chu et al.9,10 It was shown that with hexyl, dodecyl, and tetradecyl sulfates, PDADMAC forms hexagonal supramolecular stuctures with a periodicity of about 2 times the surfactant molecular length. With decyl sulfate, a cubic structure with a periodicity of ∼4 times the surfactant molecular length is formed. In a study of phase-separated complexes formed by cationically modified starch (CS) and sodium alkanoates, Merta et al. obtained analogous results.11 Merta et al. also investigated the structure of alkanoate/ CS complexes in dilute aqueous solutions by small-angle neutron scattering (SANS).12 They found that cylindrical aggregates akin to the inclusion complexes found in amylose/surfactant systems are formed, in which a core of surfactant is surrounded by helical CS chains. This paper presents a study of the structure of partially neutralized PDADMAC/sodium palmitate complexes. The goal was to clarify the structure of the surfactant domains and the influence of the surfactant association on the conformation of the polymer. This was of interest because a detailed structure of the complexes remains unknown (the extensive previous studies notwithstanding) and because it would facilitate direct comparison of complexes formed by the conformationally relatively unrestricted (7) Zhang, H.; Li, Y.; Dubin, P.; Kato, T. J. Colloid Interface Sci. 1996, 183, 546. (8) Rigsbee, D. R.; Dubin, P. L. Langmuir 1996, 12, 1928. (9) Sokolov, E. I.; Yeh, F.; Khokhlov, A.; Chu, B. Langmuir 1996, 12, 6229. (10) Sokolov, E. I.; Yeh, F.; Khokhlov, A.; Grinberg, V. Ya.; Chu, B. J. Phys. Chem. B 1998, 102, 7091. (11) Merta, J.; Torkkeli, M.; Ikonen, T.; Serimaa, R.; Stenius, P. Macromolecules 2001, 34, 2937. (12) Merta, J.; Garamus, V. M.; Kuklin, A. I.; Willumeit, R.; Stenius, P. Langmuir 2000, 16, 10061.

10.1021/la011867t CCC: $22.00 © 2002 American Chemical Society Published on Web 08/16/2002

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PDADMAC with those formed by the CS whose structure is markedly helical. Materials and Methods Chemicals. PDADMAC from Allied Colloids, Inc., was fractionated by size exclusion chromatography (SEC) to yield a polymer with mean molecular weight of around 300 000. The distribution was very broad, from 50 000 to 500 000. Its density in aqueous (5 wt %) solutions was measured with an Anton Paar digital density meter DMA 40, Graz, Austria, and was found to be 1.5 g/mL. Surfactants. Sodium palmitate (sodium hexadecanoate, C15H31COONa, NaPal) was synthesized by neutralizing the corresponding acid (purum grade from Fluka AG) in an alcoholic solution with sodium hydroxide. The salt was purified by recrystallization from acetone. The deuterated surfactant was synthesized in the same way as the protonated one from deuterated carboxylic acid (C15D31COOH, 98% D). The deuterated acid was neutralized with NaOD in C2H5OD. All deuterated chemicals were supplied by Medical Isotopes, Inc., USA. Other Chemicals. The deuterium oxide was 99.9% D2O from Sigma. All other chemicals were analytical grade and were used without further purification. Surfactant/Polymer Mixtures. Solutions were prepared by mixing 0.35 wt % (∼0.2 vol %) PDADMAC with 8 mM protonated or deuterated NaPal (∼0.22 vol %) in heavy water. The charge ratio between polymer and surfactant was approximately 2:1. The NaPal concentration was well above critical aggregate concentration (cac ∼ 0.1 mM) and critical micelle concentration (cmc ) 1.6 mM). Under these conditions, practically all of the surfactant ions are adsorbed by PDADMAC.13 One could expect to observe a large number of soluble polymer-surfactant aggregates. Solutions were transparent and stable during experimental times of up to 48 h. Before SANS measurements, the solutions were kept for 12 h at 70 °C. Additional solutions (PDADMAC/heavy water, PDADMAC/NaCl/heavy water, NaPal/ heavy water, and NaPal/NaCl/heavy water) were prepared in the same way. Neutron Scattering. Small-angle neutron scattering experiments were made with the SANS1 instrument at the FRG1 research reactor at GKSS Research Centre, Geesthacht, Germany. The neutron wavelength was 8.5 Å. The range of scattering vectors (0.007 < q < 0.25 Å-1, q ) 4π sin θ/λ, where 2θ is the scattering angle and λ is the neutron wavelength) was obtained using four sample-to-detector distances (0.7-7 m). The wavelength resolution was 10% (full width at half-maximum). The samples were kept at 70 ( 1 °C in quartz cuvettes with a path length of 2 mm. This temperature is above the Krafft temperature of NaPal. The raw spectra were corrected for backgrounds from the solvent, sample cell, and other sources by conventional procedures.14-17 The two-dimensional isotropic scattering spectra were azimuthally averaged, converted to an absolute scale, and corrected for detector efficiency by dividing by the incoherent scattering spectrum of pure water, which was measured with a 1 mm cell.14-17 For each instrumental setting, the scattering curves were smeared by the appropriate resolution function. The calculated scattering intensity was fitted to the experimental results by means of least-squares analysis, and the errors of parameters were calculated by conventional methods.14-17

Results and Analysis First, the PDADMAC/D2O, NaPal(H)/D2O (the H means protonated surfactant), and PDADMAC/NaPal(H)/D2O mixtures were measured and compared (Figure 1). Binary solutions PDADMAC/D2O and NaPal(H)/D2O show a max(13) Mironov, A. V.; Starodubtsev, S. G.; Khokhlov, A. R.; Dembo, A. T.; Yakunin, A. N. Macromolecules 1998, 31, 7698. (14) Wignall, G. D.; Bates, F. S. J. Appl. Crystallogr. 1986, 20, 28. (15) Pedersen, J. S.; Posselt, D.; Mortensen, K. J. Appl. Crystallogr. 1990, 23, 321. (16) Bevington, B. R. Data Reduction and Error Analysis for Physical Sciences; McGraw-Hill: New York, 1969. (17) Pedersen, J. S. Adv. Colloid Interface Sci. 1997, 70, 171.

Figure 1. SANS patterns from binary solutions: 0.35 wt % PDADMAC/D2O (empty squares, solid line; model fit by eq 2, the vertical line at the X-axis shows the qmin of the fit interval), 8 mM NaPal(H)/D2O (empty triangles, solid line; model fit by two-shell particles with screened Coulomb potential, ref 12), and the ternary solution PDADMAC/NaPal/D2O (filled squares; the same concentration of polymer and surfactant as in binary solutions).

imum at the low q region, and scattering from NaPal(H)/ D2O is larger (∼3 times) than that from PDADMAC/D2O solutions. The maximum in scattering patterns can be attributed to strong electrostatic repulsion among polymer molecules and micelle aggregates due to dissociated polymer and surfactant molecules. The scattering intensities are proportional to the mass of aggregates and to the square of the contrast between neutron scattering length densities of the aggregates and the solvent; therefore, the larger scattering of surfactant solution could be connected to the higher contrast of NaPal(H)/D2O and/ or higher weight of surfactant micelles than PDADMAC/ D2O aggregates. The ternary solution exhibits a strong interaction between polymer and surfactant. The maximum at a low q region disappears, showing that oppositely charged surfactant micelles (or surface active anions of surfactant molecules) and polymer molecules screen repulsive electrostatic interaction between each other. Also, the scattering intensity dramatically increases. Even at the region of intermediate q, where the effect of electrostatic interaction in binary solutions of PDADMAC/D2O and NaPal(H)/D2O is not so strong, the ratio between scattering of the ternary solution and the binary one is around 5. If one supposes that there is no change of conformation of polymer and micelle structure, this ratio should be not more than 2. For this reason, one could suppose the significant changes of the conformation of polymer and/or size-shape of surfactant aggregates (micelles) in the ternary solution to compare with the aggregate structure in the binary solutions. Before discussing the detailed analysis of scattering data from the ternary solution, we would like to get an idea which polymer or surfactant part of the mixture could produce the observed changes in scattering intensities. The binary solution NaPal(H)/D2O should be the easiest to analyze. The observed maximum corresponds to interaction among charged micelles. We have performed the same analysis as in our previous paper12 which consists of fitting (Figure 1) the scattering patterns by two-shell ellipsoids of rotation with the screened Coulomb potential model as micelle aggregates. At this low surfactant

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concentration (5 × cmc), we observe the spherical micelles with an aggregation number of 95 ( 5, a radius of 22 ( 2 Å, and a degree of dissociation of surfactant molecules in the micelle of 0.16 ( 0.01. The obtained parameters suggest that there are small charged spherical micelles in the binary solution NaPal(H)/D2O. In the case of PDADMAC/D2O, the situation of analysis is quite difficult. One should decide if the observed maximum reflects the interaction among separate polymer molecules or if it is interaction between different parts within a single polymer molecule. The most probable explanation is that the observed maximum represents the mean distance between cylindrical-like polymer molecules in the semidilute concentration regime. One could expect this because our polymer is a highly charged linear polymer. If this is the case, there is a relation between maximum position qmax, correlation length ξ, and volume fraction of polymer φ as18,19

ξ)

2π π ) rCS qmax φ

()

1/2

(1)

where rCS is the cylindrical cross section of polymer molecules. After calculation, we obtained a radius of cylindrical cross section of 5 ( 2 Å. This value seems reasonable. To prove this result, we have fitted larger q (q > 0.04 Å-1) data using a cylindrical model. In this interval of scattering vectors, one could expect a very small influence of interaction among aggregates in the scattering data. The scattering cross section is written as

dΣ(q)/dΩ ∼ π/2 sin(qL/2 cos β)2J1(qrCS sin β)

∫0

[

(qL/2 cos β)(qrCS sin β)

]

2

sin β dβ (2)

where L is cylinder length. Fitting (Figure 1) gives the radius of cross section as 16 ( 1 Å which is higher than that obtained from eq 1 but could be considered as a moderate agreement due to the simplifications of the model (eq 2). Further analysis of the maximum in PDADMAC/D2O is the study of the dependence of qmax versus polymer concentration. This should be qmax ∼ c1/2 (eq 1) if one observes the correlation between cylindrical polymer molecules. The set of experiments which varied the concentration of polymer gave the dependence of maximum position on polymer volume fraction shown in Figure 2. The obtained dependence of maximum position versus concentration of polymer agrees perfectly with the prediction of the interaction between cylindrical-like polymer molecules. The average polymer mass is high; that is why one should check the possibility that the observed maximum is connected to the correlation length ξ ≈ 200 Å (eq 1) within one polymer molecule. We expect that the average length of a polymer molecule is around a few thousand angstroms. But in this case, the position of the maximum should be practically independent from polymer concentration, which is not consistent with data from Figure 2. To summarize the analysis of scattering data from the PDADMAC/D2O solution, one could explain the observed (18) Boden, N. In Micelles, membranes, microemulsions and monolayers; Gelbert, W. M., Ben-Shaul, A., Roux, D., Eds.; Springer-Verlag: New York, 1994. (19) Chen, S. H.; Sheu, E. Y.; Kalus, J.; Hoffmann, H. J. Appl. Crystallogr. 1988, 21, 751.

Figure 2. Analysis of SANS scattering maxima at various PDADMAC concentrations. Data are shown for the maximum position qmax as a function of PDADMAC concentrations in wt %, and the solid line is the model dependence qmax ∼ c0.5.

maximum as interaction among cylindrical-like polymer molecules which reflects the mean distance between molecules. By adding the surfactant to the polymer solution or the polymer to the solution of surfactant, one changes the electrolyte strength of solutions. That is why one has to check the possibility that observed strong increasing SANS in the ternary solution PDADMAC/NaPal(H)/D2O could be the result of the growth of surfactant micelles with increasing electrolyte strength of solution and/or of the changes in polymer conformation without the formation of common polymer/surfactant aggregates. One should try to simulate what will happen if the electrolyte strength of solution increases. We added salt (NaCl, 8 mM) to the solutions of PDADMAC/D2O and NaPal(H)/D2O. We will call these solutions PDADMAC/NaCl/D2O and NaPal(H)/ NaCl/D2O. In Figure 3, one can compare SANS intensities from the above-mentioned solutions with that of the ternary solution PDADMAC/NaPal(H)/D2O. The changes in the conformation of polymer or micelle growth with increasing electrolyte strength of solutions (PDADMAC/ NaCl/D2O and NaPal(H)/NaCl/D2O) are smaller as compared to the observed changes in the PDADMAC/ NaPal(H)/D2O mixture. In the case of NaPal(H)/NaCl/D2O, we obtained spherical micelles with an aggregation number of 105 ( 5, a radius of 23 ( 2 Å, and a degree of dissociation of the surfactant molecules in the micelle of less than 0.02. At a much higher surfactant concentration of 100 mM without salt,12 slightly prolate (axis ratio of 2) micelles with an average radius of 35 ( 2 Å were formed. For the polymer/salt solution (PDADMAC/NaCl/D2O), we have obtained the same radius of cylindrical cross section as for the salt-free solution (eq 2). The main results of the above-mentioned experiments are that in the case of a salt-free ternary solution of oppositely charged polymer and surfactants the formation of common polymer/surfactant aggregates is observed. The surfactant molecules associate to the polymer molecules in another way as in the case of neutral polymer/aninonic surfactant solutions,20 the well-known pearl-necklace model. (20) Cabane, B.; Duplessix, R. J. Phys. 1982, 43, 1529-1542.

Complexes Formed by PDADMAC and Sodium Palmitate

Figure 3. SANS patterns from solutions: 0.35 wt % PDADMAC and 8 mM NaCl in D2O (empty squares, solid line; model fit by eq 2), 8 mM NaPal(H) and 8 mM NaCl in D2O (empty triangles, solid line; model fit by two-shell particles with screened Coulomb potential, ref 12), and the ternary solution PDADMAC/NaPal(H)/D2O (filled squares; the same concentration of polymer and surfactant as in solutions with added salt).

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Figure 5. Pair distance distribution functions of the cylindrical cross section of surfactant/polymer aggregates formed in PDADMAC/NaPal(H)/D2O (filled squares) and PDADMAC/ NaPal(D)/D2O (empty triangles). For better comparison, the integral value of pCS(r) is normalized to 1.

gregates on the length scale of 20-30 Å. The ratio between intensities at low q is approximately 30, which could reflect the larger contribution of surfactant in the scattering of complex surfactant/polymer aggregates and the difference in sign of the neutron scattering length density excess of NaPal(D) and PDADMAC in heavy water. In the intermediate q interval, the slope of the scattering curves is slightly larger than 1 (Figure 4). This indicates a rodlike geometry of the formed aggregates on the length scale of hundreds of angstroms. We put a line of slope -1 in Figure 4 for comparison. With the assumption that the studied complex polymer/surfactant aggregates are rodlike, we applied the indirect Fourier transformation (IFT)21 to the experimental data from a q range higher than 0.02 Å-1. The asymptotic behavior of the scattering function can be expressed as21

dΣ(q)/dΩ )

Figure 4. SANS patterns from solutions: PDADMAC/ NaPal(H)/D2O (filled squares) and PDADMAC/NaPal(D)/D2O (empty squares); the solid lines are model fits by two-shell rigid cylinders; the dashed line has a slope of -1.

To get more information about the structure of aggregates in ternary mixtures, a measurement with the deuterated surfactant PDADMAC/NaPal(D)/D2O was performed (Figure 4). In this case, we significantly decrease the scattering from surfactant and even change the sign of the neutron scattering length density excess ∆F. In heavy water, ∆F of protonated NaPal(H) is equal to -6.2 × 1010 cm-2 and ∆F of NaPal(D) is equal to 0.56 × 1010 cm-2. For the polymer, the exact calculation of ∆F is quite difficult due to the high hydration of the polymer molecule. One can be sure that ∆F of the polymer is the same sign and smaller than that of protonated NaPal(H). Qualitatively, the shapes of the curves for PDADMAC/ NaPal(H)/D2O and PDADMAC/NaPal(D)/D2O are similar at a low q interval up to 0.06 Å-1. The main difference appears at large q which points to the difference in the distribution of surfactant and polymer in complex ag-

(πq)2π∫ p ∞

0

CS(r)J0(qr)r

dr )

( qπ)I

CS(q)

(3)

where J0 is the zeroth-order Bessel function and ICS(q) is the cross-section scattering intensity. The cross-section pair distance distribution function pCS(r) is given by ref 22 as

pCS(r) )

∫

c ∆F(r′)∆F(r + r′)r′ dr′ 2πML

(4)

where the vectors r and r′ are lying in the cross-section plane, c is the concentration of aggregates, and ML is mass per unit length of aggregate. We obtained an estimation of the distance distribution function pCS(r) by applying the IFT method (Figure 5). The experimental data and fitted curves coincide well within the fit range of q > 0.02 Å-1. The upper limit of the r value included in the indirect Fourier transformation is chosen so that the pCS(r) converges smoothly to pCS(r) ) 0 at high r values. Doing this carefully, it is possible to estimate the pair distance distribution functions of the system without particle interaction. The diameter of the aggregates can thus be (21) Glatter, O. J. Appl. Crystallogr. 1977, 10, 415. (22) Feigin, L. A.; Svergun, D. I. Structure Analysis by Small-Angle X-ray and Neutron Scattering; Plenum Press: New York, 1987; pp 4748.

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The obtained results point to a local cylindrical structure of pure PDADMAC and PDADMAC/NaPal complexes. In the case of pure PDADMAC, this result is expected due

to the high charge of the linear polymer. Also, the moderate addition of simple salt (NaCl) does not change the local conformation of the polymer at least on a length scale of 100-200 Å. The polymer molecules are locally cylindrical with a cross-section radius of 16 Å. This value is obtained in homogeneous approximation of the cylindrical cross section. That is why one should take it with a caution. Of course, the assumptions of hydration water and of shell structure could give other values of the radius of a cross section. When long-chain surfactant is added in a solution of PDADMAC, one observes a strong interaction between opposite charged surfactant and polymer. Please note that the concentration of surfactant is below the compensated concentration and the formed aggregates are soluble and stable. Also, the shape of the scattering curves (slope slightly larger than 1) in the intermediate q region 0.010.08 Å-1 is not affected by the residual noncompensated charge of polymer/surfactant complexes. We have performed one more test measurement with a concentration of surfactant 2 times higher (16 mM), and the slope slightly larger than -1 was observed. These complex aggregates of PDADMAC/NaPal are large and cylindrical-like. The surfactant part mainly contributes to the scattering intensity. It cannot be the contribution from micelles which adsorbed to the polymer because the shape and size of the surfactant part of the polymer/surfactant aggregates (hundreds of angstroms and rodlike) are totally different from those of free micelles which form under similar conditions (radius of around 20-30 Å and spherical). Experiments with deuterated surfactant give more information about the distribution of surfactant and polymer in complex aggregates. Application of the modelindependent ITF method suggests some core-shell model with a surfactant core. Modeling the SANS data assuming a population of two-shell stiff cylinders gives the following: (1) The total radius of the cross section is in the expected length interval. The maximal diameter of the cylindrical cross section from IFT was 55 Å and that obtained from modeling was 52 Å which is larger than the length of two surfactant molecules in extended conformations. According to Tanford,24 the length of the hydrocarbon chain lc for C15 is in the range of 19.2 Å (fully extended chain) to 14.5 Å (flexible chain). The total length of the surfactant molecule with a headgroup is lc + 4 Å in the present case. The hydration of the polar headgroup has not been taken into account in these estimations. (2) The value of the inner radius (8 Å) is smaller than the minimal surfactant molecule length. One can try to get the scattering length density excess of polymer in heavy water using the ratio obtained between polymer and surfactantprotonated and surfactant-deuterated from model fit and table values of ∆F for surfactant molecules. After doing this manipulation, one gets that ∆Fsh is equal to -1.29 × 1010 cm-2 from PDADMAC/NaPal(H)/D2O data and ∆Fsh is equal to -0.23 × 1010 cm-2 from PDADMAC/NaPal(D)/ D2O data. These values were obtained after taking into account that ∆Fc is the scattering length density excess for surfactant molecules in heavy water. The small value of the inner radius and variation of ∆Fsh suggest that there is also a mixed layer of polymer/surfactant. The thickness of this mixed layer could be around 5-10 Å. (3) The aggregates are not totally stiff; most likely the polymer/ surfactant aggregates are flexible. This seems quite reasonable because the surfactant molecules partly compensate the charge of the polymer and the length of

(23) Arleth, L.; Posselt, D.; Gazeau, D.; Larpent, C.; Zemb, Th.; Mortensen, K.; Pedersen, J. S. Langmuir 1997, 13, 1887.

(24) Tanford, C. The hydrophobic effect, 2nd ed.; John Wiley & Sons: New York, 1980; pp 51-53.

directly determined from the pCS(r) as the r value where pCS(r) goes to zero. In the case of PDADMAC/NaPal(H)/ D2O, the pair distance distribution function of the cylindrical cross section exhibits a shape that is characteristic of an homogeneous cylindrical structure, and in the case of PDADMAC/NaPal(D)/D2O the shape of pCS(r) is characteristic of an inhomogeneous structure with opposite signs of the excess scattering length density of core and shell.21,23 We obtained a first estimation of the cross-section diameter from the maximum distance of approximately 55 Å (Figure 5). From pCS(r), we can calculate the integral parameter of the cross section21 such as the cross-section radius of gyration RCS,g which is given by

RCS,g )

[

]

∫0∞r2pCS(r) dr 1/2 ∫0∞ pCS(r) dr

(5)

For solutions with protonated surfactant, the obtained radius of gyration of the cylindrical cross section was equal to 16 ( 1 Å and for deuterated surfactant it was 24 ( 1 Å. These values again point to an inhomogeneous distribution of surfactant and polymer in complex aggregates. The larger value of RCS,g for the deuterated surfactant PDADMAC/NaPal(D)/D2O suggests that inside the investigated aggregates there is a surfactant part, and outside, the polymer part. Information from IFT analysis gives us the possibility to model scattering data by twoshell cylinders with the outer shell as polymer and the inner core as surfactant. The fit of experimental data is performed by the scattering function of the two-shell object as17

dΣ(q)/dΩ ∼

∫0π/2[Vc(∆Fc - ∆Fsh) f(q,L,Rc) + Vt∆Fsh f(q,L,Rt)]2 sin β dβ (6)

where Vc and Vt are the volumes of core and whole aggregate, ∆Fc and ∆Fsh are the excesses of neutron scattering length densities of core and shell in heavy water, Rc and Rt are the radii of core and whole cross section, and f(q,L,R) is the scattering function of an homogeneous cylinder with length L and radius R (eq 2). The radii of the core and the whole aggregate cross section, the length of the cylinder, and the ratio between the excess of neutron scattering length densities of the core and shell were fitted. Fitting curves are presented in Figure 4. Some deviation at low q is because aggregates are not 100% rigid cylinders. Aggregates are probably flexible. Analysis of SANS data from PDADMAC/NaPal(H)/D2O and PDADMAC/NaPal(D)/ D2O gives the same parameters of cylindrical cross section Rt ) 26 ( 1 Å and Rc ) 8 ( 1 Å. The difference in the length of cylinder values obtained from PDADMAC/ NaPal(H)/D2O and PDADMAC/NaPal(D)/D2O data is about 30%, and one could only suggest that the formed aggregates are quite long. The ratio in excess scattering length density between the shell and the core for PDADMAC/NaPal(H)/D2O is equal to 0.21 ( 0.01 and for PDADMAC/NaPal(D)/D2O is equal to -0.41 ( 0.01. Discussion

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aggregates is high. Considering a point at the low q region where the model of the stiff cylinders starts to deviate from experiment data as the inflection point25 (qin), one could get the estimation of the persistence length (lp) as

1.9 ) qinlp

(7)

and the obtained value of the persistence length is approximately 200 Å which is the same order as that for polymer-like microemulsions.26 The determination of persistence length by eq 7 is affected by intra- and intermolecular interaction effects. Thus, a much more powerful approach based on the intensive studies (renormalization group theory, Monte Carlo simulation, and scattering techniques) of Pedersen and Schurtenberger should be applied.26,27 Due to the complexity of the studied system, we cannot apply the latest development of the above-mentioned approach which includes the detailed analysis of concentration effects and electrostatics (many semiflexible chain scattering function).28 Flexibility of aggregates can be obtained by fitting of the full range of scattering curves. The scattering intensities are written in the form

dΣ(q)/dΩ ∼ SWC(q,L,lp)SCS(q,R)

(8)

where S(q,L,lp) is the single-chain scattering function for a semiflexible chain with excluded-volume effects of contour length L and persistence length lp. A detailed expression of S(q,L,lp) can be found in refs 26 and 27. SCS(q,R), which is the scattering of the cross section of semiflexible aggregates, is given by

[

]

J1(qR) qR

SCS(q,R) ) 2

2

(9)

where J1 is the first-order Bessel function. The resulting fits are shown in Holtzer (bending rod) representation qdΣ(q)/dΩ in Figure 6a,b. The model explains satisfactorily the upturn of scattering data around q ) 0.01 Å-1 which points to flexibility of formed aggregates. The modeling of scattering data from PDADMAC/ NaPal(H)/D2O and PDADMAC/NaPal(D)/D2O gives the same values of contour length of 2000 ( 200 Å and persistence length of 150 ( 20 Å. From molecular mass considerations, the average contour length of the pure polymer molecule should be around 7000 Å. The absolute value of the persistence length is smaller than that obtained by eq 7. This emphasizes the significant effect of intrachain interactions which decreases the usability of eq 7. However, one has to consider the obtained values of contour length and persistence length with a caution. The obtained values of contour length are affected by the polydispersity of the aggregates and by the interactions among the aggregates. In ref 26, the polydispersity was fixed to Mw/Mn ) 2 and then the value of an average contour length was determined by fitting. In our case, PDADMAC molecules are quite polydisperse, and we do not know the exact molecular weight distribution. Because of that, it was not possible to include polydispersity in the fitting. The persistence length is affected by interchain interac(25) Magid, L. J. J. Phys. Chem. B 1998, 102, 4064. (26) Jerke, G.; Pedersen, J. S.; Egelhaaf, S. U.; Schurtenberger, P. Phys. Rev. E 1997, 56, 5772. (27) Pedersen, J. S.; Schurtenberger, P. Macromolecules 1996, 29, 7602. (28) Cannavacciuolo, L.; Pedersen, J. S.; Schurtenberger, P. J. Phys.: Condens. Matter 2002, 14, 2283.

Figure 6. (a) Comparison of experimental data of PDADMAC/ NaPal(H)/D2O (filled squares) with theoretical curves (eq 8) in the Holtzer representation. (b) Comparison of experimental data of PDADMAC/NaPal(D)/D2O (empty squares) with theoretical curves (eq 8) in the Holtzer representation.

tions and should be extrapolated to the value at “zero concentration”. This was not done because it is not straightforward how to perform this extrapolation for the set of the measurements in polymer/surfactant solutions. The obtained values of contour length (∼2000 Å) and persistence length (∼150 Å) together with the value of the radius of the cross section (∼25 Å) look reasonable. These values support our assumption that formed aggregates are long and flexible. The structural characteristics obtained from formed PDADMAC/NaPal aggregates can be compared with the well-known pearl-necklace model proposed for poly(ethylene oxide) (PEO) macromolecules with sodium dodecyl sulfate (SDS).20,29 In this classic paper of Cabane and Duplessix,20 the adsorption of small spherical SDS micelles to polymer coils of PEO is reported. One can try to follow the above-mentioned model for the case of PDADMAC/NaPal solutions and try to explain the maximum at large q for PDADMAC/NaPal(D)/D2O (Figure 4) by interference between adsorbed spherical NaPal micelles. From the position of the maximum, the average distance between micelles should be less than 40 Å which is less than the diameter of NaPal micelles (∼45 Å). For (29) Lee, L. T.; Cabane, B. Macromolecules 1997, 30, 6559.

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this reason, one should use the core-shell model which gives the slope -1 at low q and a maximum at large q for PDADMAC/NaPal(D)/D2O solutions. The proposed coreshell semiflexible chain model explains the main features of the scattering patterns and looks very reasonable for complexes formed by oppositely charged linear polymer and surfactant. To accurately calculate the interactions between surfactant and charged polymer, one should take many contributions into consideration, which is out of the scope of the present paper. However, one can be sure that the strong electrostatic interaction between polymer and surfactant is responsible for the rebuilding of small micelles of NaPal and the formation of complex PDADMAC/ NaPal core-shell rodlike aggregates. The intensive investigations of Dubin’s group5-9 also give some arguments for the limitation of the pearlnecklace model especially when the polymer molecule is small as compared to the surfactant micelle. The research of Dubin et al. has been explained by the adsorption of the micelles to PDADMAC mainly because the electrostatic interaction is decreased by using the mixture of nonionic/ ionic surfactants and by the addition of a salt. In this case, electrostatic interaction between surfactant and polymer is not enough to rebuild the micelles and to form another kind of complex. Of course, detailed thermodynamic calculations of micelle formation and polymer/ surfactant aggregates are needed. The structure of phase-separated, electrostatically neutral, cross-linked PDADMAC/surfactant (SDS) complexes as reported by Chu et al.10,11,30,31 is hexagonal for long-chain surfactants which supports our observation of rodlike aggregates. The overall correlation size of PDADMAC gel is found to be a few thousand angstroms which is the same order of magnitude as obtained in the present study. The highly ordered structure in PDADMAC/ SDS complexes is different from those of pure SDS.30 This agrees with our observation of the formation of rodlike (30) Yeh, F.; Sokolov, E. L.; Walter, Th.; Chu, B. Langmuir 1998, 14, 4350. (31) Yeh, F.; Sokolov, E. L.; Khokhlov, A. R.; Chu, B. J. Am. Chem. Soc. 1996, 118, 4350.

Merta et al.

aggregates in PDADMAC/NaPal/water solutions which are different from pure NaPal micelles in size and shape. There are differences in the experimental conditions of our research with the studies of Chu et al.: a branched polymer, a surfactant/polymer ratio, and a solubility of formed complexes. It is very important to stress that qualitatively the results agree mainly because in both cases the strong electrostatic interaction is not screened which stimulates the formation of large polymer/surfactant aggregates. The shapes of complexes formed in PDADMAC/NaPal/ water and in cationic starch/NaPal/water12 are similar. In both cases, one observes core-shell cylindrical aggregates. However, there are also differences: the larger shell size in the case of cationic starch and the smaller size of the surfactant part when compared with PDADMAC/ NaPal aggregates. The cross-section radius of cationic starch aggregates is practically unchanged with additional surfactant. This should point to a higher rigidity of cationic starch molecules which are in a helical conformation. For this reason, one observes inclusive type complexes in the case of cationic starch and cooperative type complexes in the case of PDADMAC mixtures. Conclusion In salt-free solutions of PDADMAC and NaPal, the strong electrostatic interaction rebuilds micelles into long (∼2000 Å) rodlike complex aggregates of polymer and surfactant. The cross section of aggregates (diameter, 5055 Å) has a shell structure with an inner surfactant core and an outer polymer shell. There is also a mixing layer between polymer and surfactant. Aggregates are flexible (persistence length of the order of 150 Å). Acknowledgment. The authors are thankful to Professor J. S. Pedersen for the fitting routine of the scattering from semiflexible chains. Also, research assistant Tekla Tammelin is thanked for laboratory assistance. LA011867T